I have found von Beckerath's Handbuch der ägyptischen Königsnamen extremely useful (I was using it just yesterday).

I would like to highlight an article of von Beckerath's which I have found extremely helpful. Jürgen von Beckerath, "Die Lesung von "Regierungsjahr": ein neuer Vorschlag," Zeitschrift für ägyptische Sprache und Altertumskunde 95/2 (1969): 88-91. In this article von Beckerath establishes that the reading of the regnal year group is ḥsbt, not ḥ3t-zp or rnpt-zp. This reading was confirmed in Kaul-Theodor Zauzich, "Das topographische Onomastikon im P. Kairo 31169," Göttinger Miszellen 99 (1987): 83-91.

It was also von Beckerath who pointed out that we really have no evidence that the Egyptians knew about the Sothic cycle before the Ptolemaic period.

It has been at least a decade since von Beckerath was active in the field, but he made some important contributions.

Wednesday, June 29, 2016

Hans Fiene is a Lutheran pastor in Illinois. I am disappointed with his anti-Mormon tendencies but I appreciate his thoughtfulness. In this video, however, he makes a point that I have often heard my friend, Lou Midgley, make:

You cannot make a popular explanation of the Christian Trinity of the creeds without falling into heresy.

From my perspective, the formulations of the creeds tend to be incoherent gibberish, and I appreciate a good Lutheran pastor being able to articulate this. Perhaps there is some common ground we can build on.

Saturday, June 18, 2016

So how many books did the typical preexilic Israelite own? By books, we mean literary works or works of knowledge, not things like tax receipts and property deeds.

If I had to guess, I think that it would be pretty safe to say that the mode was zero. That means that a majority of ancient Israelites could not read and did not personally own any books. But some percentage of ancient Israelites could read. Some percentage of them did own literary texts or works of knowledge. Again, the absolute percentage need not be large, but chances are that if you were privileged enough to read, you probably wanted to possess something to read.

Unfortunately, we cannot answer that question, but we can get some idea by looking at ownership of literary works in the Neo-Assyrian empire. SAA VII 49-51 are three lists of tablets owned by various individuals in the Neo-Assyrian empire. The texts are somewhat fragmentary, but they typically list the works and how many tablets in the work, and a summary of the number of tablets accompanied by the name of the individual. Taking the entries where the total number of tablets owned is more or less intact in all of the texts, we get the following list (in ascending order by tablet):

Aplaya owned 1 tablet

Mushezib-Nabu owned 1 tablet

Tabni owned 2 tablets

Nabu-balassu-iqbi owned [x]+2 tablets

Nabu-shum-[. . .] owned [1]5 tablets

Assur-mukin-pale'a owned [1]8 tablets

Shamash-eriba owned 28 tablets

Nabu-shakin-shulmi owned [x]+37 tablets

[...] owned 100+[x] tablets

Arraba owned 185 tablets

Nabu-nadin-apli owned 188 tablets

Nabu-[. . .] owned 435 tablets

What is interesting about this list is the spread. About a third of those who owned tablets owned only one or two. About a third of them more than dozen tablets. About a third owned more than a hundred tablets. Remember these are literary texts or works of knowledge (the ancient equivalent of scientific literature). The average of those whose numbers are completely intact is 120 tablets.

I would expect ancient Israelite personal libraries to show a similar spread. Some would only own a work or two. Some would have several. What is somewhat surprising is that multiple individuals had extensive libraries, the equivalent of dozens of scrolls. We should suppose that ancient Israel would be the same.

It would be nicer to have a larger sample size. It would be nice if we had equivalent lists from Israel. But based on the information we do have, highly literate individuals with large libraries are known from pre-exilic Israelite times.

Wednesday, June 8, 2016

Mathematical models can be great. They do, however, have some
limitations. Suppose, for example, that you are trying to predict some
data that you suspect has some mathematical relationship and you want to
know the future behavior. A mathematical model might be useful to
predict the future results of the data. Your predictive abilities will
only be as good as the model (or formula) that you are using.
Presumably, if your model accounts for past data, it should work for
future data as well. We'll keep this fairly simple.

Lets
say that you start with an initial condition and it starts at zero. The
next data point to come out is a one. So at x = 0, y = 0 and x=1, y=1.
This gives us a nice formula: x = y. We are ready to predict the future.
Our guess is that when x = 2, y =2. Our graph of the function looks
like this:

This
provides nice steady increase. If it is a graph of your investments,
you will not be getting rich very quick, but you might not be getting
poor either. If it is global temperatures, it might cause some concern.
If it is crop yields per square meter, then it is steady and
predictable.

But when x =2 comes out, it turns out
that y = 0. Our prediction was off by 2. Our graph comparing our
prediction with actual results looks like this:

This
looks like a simple problem to fix. We simply change our equation to y =
-x^2 + 2x. This equation also works for the first three values. Our
graph comparing our prediction with actual results now looks like this:

Those
curves are pretty close. We seem to be on the right track. Let's expand
our prediction graph and predict what is going to happen in the future:

We
predict that the next point on the graph will be -3. It looks as though
the graph is going increasingly downward. If this is your return on
investment, then it looks like you better get out of the market now. If
this is global temperatures, then stock up on winter clothes.

In fact, the next point is -1. Again, we are off by 2. Out graph comparing our prediction with actual results looks like this:

This is a not so easy fix. We change our equation to y = (x^3)/3 - 2x^2 + 8x/3. This gives us the following graph:

This is not exact but it is close. If we look down the road, we can predict the following:

So
if this is our investments, we should just ride it out because things
look better down the road. If it is global temperatures, then hang on
because things will get a lot hotter really quick.

When the next number comes in, it comes in as 0, exactly as our model predicted:

Surely, we are on the right track.

The next number, however, comes in as 1 rather then the 5 our model predicted.

Something is wrong again. If we look at our various model graphs, we can see that they end up going all over the place:

Clearly,
while each of these graphs works for a bit, they all fail in the end.
They all end up flying off on a tangent. This is even more clear when we
look at the long term trajectories:

All
of these graphs were based on the actual data, but they differ markedly
in their projections (all of which turn out to be wrong in the long
term). Remember that the extreme models accounted for almost the same
range of data, but after a point made widely divergent predictions.

So,
one take away is that the models, at some point, break down. We could
make the models much more complicated and account for the first twenty
points but they would then still go wildly wrong. The general point
would remain. If you are looking at a fluctuating phenomenon and
suddenly your model becomes monotonically increasing or decreasing (that
is, it stops fluctuating) then that is the point where your model
probably has broken down.